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📁 利用FPGA实现浮点运算的verilog代码 希望能够给需要做这方面研究的同仁有所帮助
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<P class=pediy><FONT color=blue>标 题:</FONT>浮点运算简介(part I)... (6千字)<BR><FONT 
color=blue>发信人<SPAN class=pediy>:</SPAN></FONT><SPAN class=pediy>hume<BR><FONT 
color=blue>时 间:</FONT>2002-3-31 8:48:40<BR><FONT 
color=blue>详细信息:</FONT><BR></SPAN></P>
<BLOCKQUOTE><SPAN class=pediy>浮点运算简介 <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Hume/冷雨飘心 <BR><SPAN 
  class=pediy><BR>对于习惯于C的灵活多变的数据类型和方便的计算那些人而言,了解底层的浮点运算似乎没有什么意义,现在Visual盛行的时代还有多少人关心那些所谓的底层呢? 
  <BR>对了AfOs来说,浮点运算是编程中很重要的一部分,因为我们可能会面临一些稍微复杂的运算,如果你和我一样是Die-hard的asm拥护者,不想轻易用C来解决问题,你肯定能想像在asm下用整数运算求sin(2.3)的痛苦,实际上,微机早就为我们准备了解决之道:那就是浮点运算.但现在关于浮点运算的资料较少,相信很多人和我一样还不掌握这种强有力的技术,那好,我们一起来学习学习. 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; <BR><BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (一)浮点数 <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (This Part mainly Froe Bill's 
  Article) <BR>在这之前,先来看几个术语: <BR>FPU-&gt;Floating Point Unit,浮点运算部件 
  <BR>BCD-&gt;Binary Coded Decimal 
  压缩的二十进制数,是用4个位来表示数字0~9,一个byte表示两个十进制数,比如01111001表示89 
  <BR>科学计数法:这是科学的~~~~具体含义查查初中还是小学的数学课本 D:) <BR><BR>浮点运算使用三种不同的数据: <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; 1)整数(Integer),又分为字,短整数(Short Integer)和长整数(Long Integer) 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; 2)实数(Real)分单精度(Single Real)和双精度(Double Real) 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; 3)压缩的二十进制数(BCD) <BR>&nbsp; &nbsp; <BR>&nbsp; 
  &nbsp; 下面是其位数(bits)和能表示的大致范围和 <BR><BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  Type&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Length&nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; Range <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  ----------------------------------------------- <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; Word Integer&nbsp; &nbsp; 16 bit&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  -32768 to 32768 <BR>&nbsp; &nbsp; &nbsp; &nbsp; Short Integer&nbsp; 32 
  bit&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -2.14e9 to 2.14e9 <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; Long Integer&nbsp; &nbsp; 64 bit&nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; -9.22e18 to 9.22e18 <BR>&nbsp; &nbsp; &nbsp; &nbsp; Single Real&nbsp; 
  &nbsp; 32 bit&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1.18e-38 to 3.40e38 <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; Double Real&nbsp; &nbsp; 64 bit&nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; 2.23e-308 to 1.79e308 <BR>&nbsp; &nbsp; &nbsp; &nbsp; extended 
  Real&nbsp; 80 bit&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3.37e-1932 to 1.18e4932 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; Packed BCD&nbsp; &nbsp; &nbsp; 80 bit&nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; -1e18 to 1e18 <BR><BR>双精度数和扩展精度数表示范围对一般应用来说已经足够大了! 
  <BR><BR>1)整数,以补码形式存储,正数的补码是其本身,负数补码是其绝对值的各位变反后加1,下面是实际存储的例子: <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; 0024&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var1 dw 24 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; FFFE&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  var2 dw -2 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 000004D2&nbsp; &nbsp; &nbsp; &nbsp; 
  var3 dd 1234 <BR>&nbsp; &nbsp; &nbsp; &nbsp; FFFFFF85&nbsp; &nbsp; &nbsp; 
  &nbsp; var4 dd -123 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 0000000000002694var5 dq 
  9876 <BR>&nbsp; &nbsp; &nbsp; &nbsp; FFFFFFFFFFFFFEBFvar6 dq -321 
  <BR><BR>2)BCD数 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  在FPU中用80位表示正好是浮点堆寄存器的宽度,在其格式如下存储: <BR>&nbsp; &nbsp; Bit <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; 79___72_71________________________________________0 <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; 符号&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  ---18个二十进制数-------- <BR>看下面的例子: <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  00000000000000012345&nbsp; &nbsp; &nbsp; &nbsp; var1&nbsp; dt&nbsp; &nbsp; 
  12345 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 80000000000000000100&nbsp; &nbsp; &nbsp; 
  &nbsp; var2&nbsp; dt&nbsp; &nbsp; -100 <BR><BR>3)浮点数,这个复杂点,有三种格式 
  <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; 单精度:_31_30________23_22___________0 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 符号&nbsp; &nbsp; 指数&nbsp; 
  &nbsp; &nbsp; &nbsp; 有效数 <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  双精度:_63_62__________52_51__________________0 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; 符号&nbsp; &nbsp; 指数&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; 有效数 <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; 扩展精度数: <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; _79_78____________64_63___________________0 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 符号&nbsp; &nbsp; 指数&nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 有效数 <BR>例子: <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; C377999A&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; var1&nbsp; dd&nbsp; &nbsp; &nbsp; -247.6 <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; 40000000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; var2&nbsp; dd&nbsp; &nbsp; &nbsp; 2.0 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  486F4200&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  var3&nbsp; real4&nbsp; 2.45e+5 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  4059100000000000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var4&nbsp; dq&nbsp; 
  &nbsp; &nbsp; 100.25 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 3F543BF727136A40&nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var5&nbsp; real8&nbsp; 0.00123 
  <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; C377999A&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var1&nbsp; dd&nbsp; &nbsp; &nbsp; -247.6 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; 40000000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var2&nbsp; dd&nbsp; &nbsp; &nbsp; 2.0 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; 486F4200&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var3&nbsp; real4&nbsp; 2.45e+5 <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; 4059100000000000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  var4&nbsp; dq&nbsp; &nbsp; &nbsp; 100.25 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  3F543BF727136A40&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; var5&nbsp; 
  real8&nbsp; 0.001235 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  400487F34D6A161E4F76&nbsp; &nbsp; &nbsp; &nbsp; var6&nbsp; real10&nbsp; 
  33.9876 <BR><BR>DD和real4都可以在asm中来定义单精度浮点数,4 bytes 
  <BR>DQ和real8都可以在asm中来定义双精度浮点数,8 bytes <BR>DT和real10都可以在asm中来定义扩展精度浮点数,10 bytes 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; (二)浮点部件 
  <BR><BR>FPU从功能上分为两个部分:控制单元和运算单元,控制单元主要面向CPU,而算数单元负责具体算数运算. 
  <BR>FPU即浮点部件包括8个通用寄存器,5个错误指针寄存器和三个控制寄存器. <BR><BR>1)8个通用寄存器每个80 
  bit,形成一个寄存器堆栈,所有的计算结果都保存在寄存器堆栈中,其中数据全部是80位的扩展精度格式,即使是BCD,整数,单精度和双精度等在装入寄存器的时候都要被FPU自动转化为80位的扩展精度格式,注意栈顶通常表示为ST(0),然后是ST(1)...ST(i),ST(i)是相对于栈顶而言的. 
  <BR><BR>和堆栈很相似,只不过宽度为80bit,映像如下: <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; _______________________ <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; ST(0)&nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; |&nbsp; &nbsp; &nbsp; <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; |_______________________| <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; ST(1)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; | 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |_______________________| 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; 
  ......&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; | <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; ......&nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; | <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; 
  &nbsp; &nbsp; &nbsp; ST(i)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; <BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; |_______________________| <BR><BR>2)控制寄存器,FPU有三个控制寄存器:状态寄存器,控制寄存器和标记寄存器 
  <BR><BR>状态寄存器-&gt;SW <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  _M_____D________10___9____8___7_________5_________________________0__ 
  <BR>&nbsp; &nbsp; &nbsp; |&nbsp; B |&nbsp; C3| TOP| C2 | C1 | C0 | ES |&nbsp; 
  &nbsp; | PE | UE | OE | ZE | DE | IE | <BR>&nbsp; &nbsp; &nbsp; 
  |____|____|____|____|____|____|____|____|____|____|____|____|____|____| 
  <BR><BR>B:&nbsp; &nbsp; 浮点部件正忙 <BR>C0-C3&nbsp; 指示浮点运算的结果,不同指令有不同含义 
  <BR>TOP&nbsp; &nbsp; 指示栈顶,通常是0 <BR>ES 以下任何位置位 (pe, ue, oe, ze, de, or ie) 则置位 
  <BR>PE 精度故障&nbsp; <BR>UE 数字太小无法表示溢出&nbsp; <BR>OE 现有精度无法表示,数字太大溢出&nbsp; <BR>ZE 
  除0错&nbsp; <BR>DE 指示至少有一个操作数未规格化&nbsp; <BR>IE 无效错误,指示堆栈上溢或下溢,无效操作数等 
  <BR><BR><BR>控制寄存器: <BR>&nbsp; &nbsp; &nbsp; &nbsp; 
  _15____________10___9____8___7_________5______________________0__ <BR>&nbsp; 
  &nbsp; &nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |IC | RC | 
  PC&nbsp; |&nbsp; &nbsp; | PM | UM | OM | ZM | DM | IM | <BR>&nbsp; &nbsp; 
  &nbsp; |____|____|____|___|__|_|__|__|____|____|____|____|____|____|____| 
  <BR><BR>IC 无穷大控制,对486,已经无效 <BR>RC 舍入控制 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 00 = 
  朝最接近或者偶数舍入 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 01 = 朝负无穷大方向舍入 <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; 10 = 朝</SPAN></SPAN><SPAN class=pediy>正无穷大方向舍入 <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; 11 = 超0方向截断 <BR>PC 精度控制 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 00 = 单精度 
  <BR>&nbsp; &nbsp; &nbsp; &nbsp; 01 = 保留 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 10 = 
  双精度 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 11 = 扩展精度 <BR>PM~IM 屏蔽状态寄存器低5位指示的错误.为1则屏蔽. 
  <BR><BR><BR>标记寄存器: <BR>&nbsp; &nbsp; &nbsp; &nbsp; 每2 
  bit表示一个对应堆栈寄存器的状态,具体含义如下: <BR>&nbsp; &nbsp; &nbsp; 
  15________________________________________3_____0 <BR>&nbsp; &nbsp; &nbsp; 
  |Tag7 |...................................|tag1| <BR>&nbsp; &nbsp; &nbsp; 
  |_____|___________________________________|____| <BR>&nbsp; &nbsp; &nbsp; 
  &nbsp; <BR>含义: <BR>&nbsp; &nbsp; &nbsp; &nbsp; 00 = 有效 <BR>&nbsp; &nbsp; 
  &nbsp; &nbsp; 01 = 零 <BR>&nbsp; &nbsp; &nbsp; &nbsp; 10 = 无效或无穷大 <BR>&nbsp; 
  &nbsp; &nbsp; &nbsp; 11 = 为空 <BR><BR>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
</SPAN></BLOCKQUOTE>
<BLOCKQUOTE><SPAN class=pediy>(三)浮点指令系统及MASM下浮点程序设计 
  <BR><BR>事实上最重要和比较难于找到资料在(一)和(二)部分中已经介绍,下面是为了完整性的考虑,如果你是第一次接触浮点指令,看看下面的摘要也无妨.另外本文未涉及到的一个方面是关于浮点处理异常的情况,因为涉及到保护模式和中断、任务切换以及SEH等较多内容,我相信介绍之后只会令人更加迷惑,况且我现在似乎也无法把这几个问题完全说清除,一般我们几乎不需要知道这些.让我们先来看主要内容. 
  <BR><BR>关于浮点程序设计是一个大的话题,我只是提纲挈领地简述Masm32V7(/V6)中的设计方法,因为486以上的CPU内建了浮点部件所以可以在程序里直接使用浮点指令.下面是一个小例子: 
  <BR><BR>__MASMSTD&nbsp; equ&nbsp; &nbsp; 1 <BR>.386p <BR>.model flat, stdcall
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